Spin susceptibility of stabilized delta phase in the Pu-Ga alloy is studied by measuring Ga-69,Ga-71 NMR spectra and nuclear spin-lattice relaxation rate T-69(1)-1 in the temperature range 5-350 K. The shift (K-69) of the 69,71Ga NMR line and T-69(1)-1 are controlled, correspondingly, by the static and flu.ctuating-in-time parts of the local magnetic field arisen at nonmagnetic gallium due to transferred hyperfine coupling with the nearest f-electron environment of more magnetic Pu. The nonmonotonic behavior of K-69(T) proportional to chi(s,5f)(T) with a maximum around 150 K is related to the peculiarities in temperature dependence of the f-electron spin susceptibility X,,5 T) in 45 phase of plutonium. The observed reversibility in temperature of 69K(T) provides strong evidence for the development with decreasing T of instability in f-electron bands near the Fermi energy. Such an electronic instability is accompanied with a pseudogap-like decrease of chi(s,5f)(T) at T < 150 K, whereas a gradual increase in the width of central line with decreasing T shows the growth of the short-wave static contributions to spin susceptibility of stabilized delta-Pu down to the lowest temperature. However, no NMR evidence favoring the formation of the static magnetic order in delta-Pu was observed down to 5 K. Below 200 K, the product (T1T)(-1) increases as temperature decreases down to 80 K, which was considered as an indication that the growth of the intensity of the f-electron spin fluctuations near Larmor frequency with decreasing T is favored. At lower temperature, the growth of (T1T)(-1) is saturated, and the temperature of the crossover between the two different regimes of spin fluctuations is close to the characteristic Kondo temperature of the order of 100 K as estimated on the basis of the resistivity and specific heat data for stabilized delta-Pu.